You are probably already familiar with the concept of the absolute value of a number, but I'm going
to give you both a bad definition, which works some of the time and a much better definition that generalizes
to all kinds of numbers that you might encounter in the future in math.
So here is a bad way of explaining what the absolute value means.
So we could say and this is something you might have learned, you know, when you were in elementary
school, that the absolute value of a no means to strip off the negative sign if it has a negative sign.
So you have the absolute value of minus four.
You just dropped the minus sign in.
The absolute value is four.
Now, the thing is that that works sometimes for real numbers.
That actually does work.
But that's not the best definition.
It's not the best way to think about the absolute value.
A better explanation is that the absolute value of a number is the distance of that number to the origin
of the number line.
Now, these two explanations are compatible for some types of numbers, but they are incompatible for
other types of numbers.
And this is always the correct explanation, is always the correct definition and not necessarily this
one.
So for real numbers, we think of real numbers as being on a line with zero in the middle.
So the absolute value of the number two is the distance away from the origin, which is two units.
Likewise, the absolute value of minus five is five because the distance from minus five to the origin
is five units.
Now where the definition of just dropping them minus sign breaks down is when you are working with complex
numbers where you have a real part and an imaginary part.
You don't have to worry about that in this course.
We're not going to be working with or incorporating complex value numbers in this course.
Nonetheless, I think it's useful to have a more accurate definition of the absolute value, which is
also applicable to other kinds of numbers.
There are two kinds of notation for indicating the absolute value of a number.
You can see.
So when you do like chalkboard math, if you're writing math down in pen and on a piece of paper, you're
likely to see this notation where you have these vertical bars surrounding the number or in this case,
the variable.
You might also see it written up a B.S. for absolute value.
And then in parentheses, the number or the variable that you're taking, the absolute value of this
notation is how it would look in computer code.
And this is probably how it would look in the slides or, you know, in a math textbook.
So quick video, I introduce you to absolute value.
And I hope it was a good reminder of a bad definition of absolute value and a more accurate definition
of absolute value.